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Sojourn Times in Finite Markov Processes

Gerardo Rubino and Bruno Sericola
Journal of Applied Probability
Vol. 26, No. 4 (Dec., 1989), pp. 744-756
DOI: 10.2307/3214379
Stable URL: http://www.jstor.org/stable/3214379
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Sojourn Times in Finite Markov Processes
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Abstract

Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the nth sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases. We consider the usually pseudo-aggregated Markov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions in the original Markov process and the moments of the corresponding holding times of the pseudoaggregated one is also studied.

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